Game or puzzle type amusement devices, other than jigsaw type puzzles, wherein a multitude of pieces interact, or are otherwise mutually arranged, with respect to each other such that particular indicia provided upon the pieces are disposed within a particular or predetermined pattern, array, design, or the like, are of course well-known. The provision of the particular indicia upon the game or puzzle pieces, and the arrangement of the pieces with respect to each other, is such, however, that only one combination or arrangement of the game or puzzle pieces, with respect to an extensive number of possible specific orientations or arrangements of the game or puzzle pieces, relative to one another defines the particularly desired or required solution. This fact characteristic of such conventional game or puzzle type amusement devices having only one mode of solution often leads to a marked decline in the popularity of such game or puzzle type amusement devices for the obvious reason that once the player discovers the sole solution to the game or puzzle, or more particularly, once the player has solved the game or puzzle several times, the novelty of the game or puzzle is considerably diminished with the result that the player no longer has a strong interest in, or attraction to, the game or puzzle.